If there is only one Critical Point, it must be the Extremum for functions of one variable. There are
exceptions for two variables, but none of degree . Such exceptions include

(Wagon 1991). This latter function has discontinuous and , and and .

**References**

Ash, A. M. and Sexton, H. ``A Surface with One Local Minimum.'' *Math. Mag.* **58**, 147-149, 1985.

Calvert, B. and Vamanamurthy, M. K. ``Local and Global Extrema for Functions of Several Variables.''
*J. Austral. Math. Soc.* **29**, 362-368, 1980.

Davies, R. Solution to Problem 1235. *Math. Mag.* **61**, 59, 1988.

Wagon, S. ``Failure of the Only-Critical-Point-in-Town Test.'' §3.4 in *Mathematica in Action.*
New York: W. H. Freeman, pp. 87-91 and 228, 1991.

© 1996-9

1999-05-26